Strongly invertible knots, equivariant slice genera, and an equivariant algebraic concordance group
Strongly invertible knots, equivariant slice genera, and an equivariant algebraic concordance group
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DOI：
10.1112/jlms.12732
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发表时间：
2022-08
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通讯作者：
Allison N. Miller;Mark Powell
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作者：
Allison N. Miller;Mark Powell
利用Blanchfield形式得到了强可逆纽结的等变片亏格的一个下界。对于我们的主要应用，设K$K$是一个强可逆亏格的单切片纽结，其多项式为非平凡的亚历山大多项式.证明了等变连通和#nK$\#^nK $的等变片亏格至少为n/4$n/4$ .我们还构造了一个等变代数和谐群，并证明了到经典代数和谐群的遗忘映射的核是无限秩的。
We use the Blanchfield form to obtain a lower bound on the equivariant slice genus of a strongly invertible knot. For our main application, let K$K$ be a strongly invertible genus one slice knot with nontrivial Alexander polynomial. We show that the equivariant slice genus of an equivariant connected sum #nK$\#^n K$ is at least n/4$n/4$ . We also formulate an equivariant algebraic concordance group, and show that the kernel of the forgetful map to the classical algebraic concordance group is infinite rank.